Obviously, I don't expect this. But I was thinking about it, and the importance, uniqueness, and irreplaceability of this payload is almost (?) unprecedented, especially for a transnational project. I don't really think there's an insurance claim that can cover the JWST. Certainly, there's an extensive investigation, but how would that even work? Would NASA sue Arianespace? Would everybody sue Arianespace? Would nothing happen--have launch contingencies already been agreed on? Does Israël make a public apology? Does Macron make a public apology? Does Arianespace ever sell a flight again? Do we all go home & sob?
This is now, fortunately, an academic question. But here is my take at answering your questions (written as if JWST hadn't launched yet):
- NASA, ESA, and Arianespace would all like be involved in the failure investigation. Ariane would normally take the lead as the rocket owner. It is possible NASA and ESA could also have independent investigations in parallel.
- I don't expect any lawsuits unless there was wilful negligence. Rockets blow up all the time. Of course the details of what actions can be taken would be in the contract, which is not public.
- There would definitely be public apologies from Ariane, but they have those whenever there is a failure.
- I don't expect Macron would apologize
- Ariane would probably sell flights again ... just like after any major failure.
- Yes, we would all be very sad.